MANOVA Calculator
Multivariate ANOVA online for free. Wilks Lambda, Pillai trace, Hotelling-Lawley, Roy and group means.
When to use it
Use when groups are compared on multiple correlated outcomes simultaneously (yield + height + tillers, behavioural battery, biomarker panel). MANOVA tests whether the treatment shifts the joint multivariate mean, controlling the family error across outcomes implicitly.
When NOT to use it
Do not use when outcomes are uncorrelated; running separate ANOVAs with FWER correction is simpler and equivalent in power. Do not use when sample size per group is smaller than the number of outcomes; the within-group covariance becomes singular. Outcomes should be on commensurable scales or standardised first.
What you get
Four classical multivariate test statistics with their F approximations and p: Wilks lambda, Pillai trace, Hotelling-Lawley trace, and Roy's largest root. Multivariate group centroids. Univariate ANOVA per outcome (the follow-up step when MANOVA is significant). Box's M test of covariance homogeneity.
How to interpret the output
Pillai's trace is the most robust to assumption violations and is the recommended default (Olson 1976). All four statistics agree when treatment effects are concentrated on one dimension; they diverge when effects spread across multiple dimensions. A significant MANOVA followed by univariate ANOVAs (with multiple-testing correction) tells you which outcomes drive the multivariate effect. Wilks lambda is the most reported statistic in agronomy and biology journals.
Common pitfalls
- Using MANOVA with too few subjects per group (singular covariance).
- Reporting only one of the four test statistics without explanation.
- Skipping Box's M (heterogeneous covariances inflate Type I error).
- Treating MANOVA as a substitute for the per-outcome univariate ANOVAs that justify the conclusions.
Try it in StatVeda
The MANOVA (multivariate ANOVA) engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open MANOVA (multivariate ANOVA)References
- Olson, C. L. (1976). On choosing a test statistic in multivariate analysis of variance. Psychological Bulletin, 83(4), 579 to 586.
- Tabachnick, B. G. and Fidell, L. S. (2013). Using Multivariate Statistics, 6th edition. Pearson, Boston.
- Hand, D. J. and Taylor, C. C. (1987). Multivariate Analysis of Variance and Repeated Measures. Chapman and Hall, London.